mirt (version 0.1-19)

bfactor: Full-Information Item Bifactor Analysis

Description

bfactor fits a confirmatory maximum likelihood bifactor model to dichotomous data under the item response theory paradigm. Pseudo-guessing parameters may be included but must be declared as constant, since the estimation of these parameters often leads to unacceptable solutions. Missing values are automatically assumed to be 0.

Usage

bfactor(fulldata, specific, guess = 0, prev.cor = NULL, par.prior = FALSE, 
  startvalues = NULL,  quadpts = NULL, ncycles = 300, EMtol = .001, nowarn = TRUE, 
  debug = FALSE, ...)

## S3 method for class 'bfactor':
summary(object, digits = 3, ...)

## S3 method for class 'bfactor':
coef(object, digits = 3, ...)

## S3 method for class 'bfactor':
fitted(object, digits = 3, ...)

## S3 method for class 'bfactor':
residuals(object, restype = 'LD', digits = 3, ...)

Arguments

fulldata

a complete matrix or data.frame of item responses that consists of only 0, 1, and NA values to be factor analyzed. If scores have been recorded by the response pattern then they can be recoded to dichotomous format u

specific

a numeric vector specifying which factor loads on which item. For example, if for a 4 item test with two specific factors, the first specific factor loads on the first two items and the second specific factor on the last two, then the vector is c(1,

guess

fixed pseudo-guessing parameter. Can be entered as a single value to assign a global value or may be entered as a numeric vector for each item of length ncol(fulldata).

prev.cor

uses a previously computed correlation matrix to be used to estimate starting values for the EM estimation

par.prior

a list declaring which items should have assumed priors distributions, and what these prior weights are. Elements are slope and int to specify the coefficients beta prior for the slopes and normal prior for the intercepts, and

startvalues

user declared start values for parameters

quadpts

number of quadrature points per dimension. If NULL then the number of quadrature points is set to 15

ncycles

the number of EM iterations to be performed

EMtol

if the largest change in the EM cycle is less than this value then the EM iteration are stopped early

object

a model estimated from bfactor of class bfactor

restype

type of residuals to be displayed. Can be either 'LD' for a local dependence matrix (Chen & Thissen, 1997) or 'exp' for the expected values for the frequencies of every response pattern

digits

number of significant digits to be rounded

nowarn

logical; suppress warnings from dependent packages?

debug

logical; turn on debugging features?

...

additional arguments to be passed

Details

bfactor follows the item factor analysis strategy explicated by Gibbons and Hedeker (1992). Nested models may be compared via an approximate chi-squared difference test or by a reduction in AIC or BIC (accessible via anova); note that this only makes sense when comparing class bfactorClass models to class mirtClass. The general equation used for item bifactor analysis in this package is in the logistic form with a scaling correction of 1.702. This correction is applied to allow comparison to mainstream programs such as TESTFACT 4 (2003). Unlike TESTFACT 4 (2003) initial start values are computed by using information from the matrix of quasi-tetrachoric correlations, potentially with Carroll's (1945) adjustment for chance responses. To begin, a MINRES factor analysis with one factor is extracted, and the transformed loadings and intercepts (see mirt for more details) are used as starting values for the general factor loadings and item intercepts. Values for the specific factor loadings are taken to be half the magnitude of the extracted general factor loadings. Note that while the sign of the loading may be incorrect for specific factors (and possibly for some of the general factor loadings) the intercepts and general factor loadings will be relatively close to the final solution. These initial values should be an improvement over the TESTFACT 4 initial starting values of 1.414 for all the general factor slopes, 1 for all the specific factor slopes, and 0 for all the intercepts. Factor scores are estimated assuming a normal prior distribution and can be appended to the input data matrix (full.scores = TRUE) or displayed in a summary table for all the unique response patterns. Fitted and residual values can be observed by using the fitted and residuals functions. To examine individuals item plots use itemplot which will also plot information and surface functions (although the plink package may be more suitable for IRT graphics). Residuals are computed using the LD statistic (Chen & Thissen, 1997) in the lower diagonal of the matrix returned by residuals, and Cramer's V above the diagonal.

References

Gibbons, R. D., & Hedeker, D. R. (1992). Full-information Item Bi-Factor Analysis. Psychometrika, 57, 423-436. Carroll, J. B. (1945). The effect of difficulty and chance success on correlations between items and between tests. Psychometrika, 26, 347-372. Wood, R., Wilson, D. T., Gibbons, R. D., Schilling, S. G., Muraki, E., & Bock, R. D. (2003). TESTFACT 4 for Windows: Test Scoring, Item Statistics, and Full-information Item Factor Analysis [Computer software]. Lincolnwood, IL: Scientific Software International.

See Also

expand.table,key2binary,confmirt

Examples

###load SAT12 and compute bifactor model with 3 specific factors
data(SAT12)
fulldata <- key2binary(SAT12,
  key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
specific <- c(2,3,2,3,3,2,1,2,1,1,1,3,1,3,1,2,1,1,3,3,1,1,3,1,3,3,1,3,2,3,1,2)
mod1 <- bfactor(fulldata, specific)
coef(mod1)

###Try with guessing parameters added
guess <- rep(.1,32)
mod2 <- bfactor(fulldata, specific, guess = guess)
coef(mod2) #item 32 too difficult to include guessing par

#fix by imposing a weak intercept prior
mod3a <- bfactor(fulldata, specific, guess = guess, par.prior =
    list(int = c(0,4), int.items = 32))
coef(mod3a)

#...or by removing guessing parameter
guess[32] <- 0
mod3b <- bfactor(fulldata, specific, guess = guess)
coef(mod3b)